Vectors - Chapter No 3

Right Answers have been shown below in red color.

1. We say that the displacement of a particle is a vector quantity. Our best justification for this
assertion is:

A) displacement can be specified by a magnitude and a direction
B) operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments
C) a displacement is obviously not a scalar
D) displacement can be specified by three numbers
E) displacement is associated with motion

2. The vectors a, b, and c are related by c = ba. Which diagram below illustrates this
relationship?

D is the Right Answer

3. A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude
of the resultant is:

A) zero
B) 1
C) 3
D) 5
E) 7

4. A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be:

A) zero
B) 3
C) 12
D) 47
E) 50

5. A vector S of magnitude 6 and another vector  have a sum of magnitude 12. The vector T:

A) must have a magnitude of at least 6 but no more than 18
B) may have a magnitude of 20
C) cannot have a magnitude greater than 12
D) must be perpendicular to S
E) must be perpendicular to the vector sum

6. The vector −A is:

A) greater than A in magnitude
B) less than A in magnitude
C) in the same direction as A
D) in the direction opposite to A
E) perpendicular to A

7. The vector V3 in the diagram is equal to:

A) V1 − V2
B) V1 + V2
C) V2 − V1
D) V1 cos θ
E) V1/(cos θ)

8. If |A + B |2 = A2 + B2, then:

A) A and B must be parallel and in the same direction
B) A and B must be parallel and in opposite directions
C) either A or B must be zero
D) the angle between A and B must be 60◦
E) none of the above is true

9. If |A + B | = A + B and neither A nor B vanish, then:

A) A and B are parallel and in the same direction
B) A and B are parallel and in opposite directions
C) the angle between A and B is 45◦
D) the angle between A and B is 60◦
E) A is perpendicular to B

10. If |AB | = A + B and neither A nor B vanish, then:

A) A and B are parallel and in the same direction
B) A and B are parallel and in opposite directions
C) the angle between A and B is 45◦
D) the angle between A and B is 60◦
E) A is perpendicular to B

11. Four vectors (A, B, C, D) all have the same magnitude. The angle θ between adjacent vectors
is 45◦ as shown. The correct vector equation is:

A) ABC + D = 0
B) B + D − √2C = 0
C) A + B = B + D
D) A + B + C + D = 0
E) (A + C )/√2 = B

12. Vectors A and B lie in the xy plane. We can deduce that A = B if:

A) A2x + A2y = B2x + B2y
B) Ax + Ay = Bx + By
C) Ax = Bx and Ay = By
D) Ay/Ax = By/Bx
E) Ax = Ay and Bx = By

13. A vector has a magnitude of 12. When its tail is at the origin it lies between the positive x axis and the negative y axis and makes an angle of 30◦ with the x axis. Its y component is:

A) 6/√3
B) −6√3
C) 6
D) −6
E) 12

14. If the x component of a vector An, in the xy plane, is half as large as the magnitude of the vector, the tangent of the angle between the vector and the x axis is:

A) √3
B) 1/2
C) √3/2
D) 3/2
E) 3

15. If A = (6 m)i − (8 m)j then 4A has magnitude:

A) 10 m
B) 20 m
C) 30 m
D) 40 m
E) 50 m

16. A vector has a component of 10 m in the +x direction, a component of 10 m in the +y direction, and a component of 5 m in the +z direction. The magnitude of this vector is:

A) zero
B) 15 m
C) 20 m
D) 25 m
E) 225 m

17. Let V = (2.00 m)i + (6.00 m)j − (3.00 m) k. The magnitude of V is:

A) 5.00 m
B) 5.57 m
C) 7.00 m
D) 7.42 m
E) 8.54 m

18. A vector in the xy plane has a magnitude of 25 m and an x component of 12 m. The angle it makes with the positive x axis is:

A) 26◦
B) 29◦
C) 61◦
D) 64◦
E) 241◦

19. The angle between A = (25 m)i + (45 m)j and the positive x axis is:

A) 29◦
B) 61◦
C) 151◦
D) 209◦
E) 241◦

20. The angle between A = (−25 m)i + (45 m)j and the positive x axis is:

A) 29◦
B) 61◦
C) 119◦
D) 151◦
E) 209◦

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